Based on the thought that the gyro might be broken or working incorrectly I decided to buy another one since it's quite cheap. But even it's another completly new one it is still not working which makes me thinking that either the arduino board works incorrectly or that it is just me being completly stupid.
So here is a second of what my setup looks like this time:

It is as simple as it could be isnt it?! Again I connected GND to GND and VCC to 5,0V. Additionally I connect SLC (green wire) to A5 and SDA (orange wire) to A4.
Using this setup I did nothing but connecting the arduino to my computer and uploading the I²C-Scanner I posted in my first post. But it is still not working. I just get the message: "No I²C device found".
So what could be wrong? Did I still connect something wrong? I mean there are just like four wires so it shouldn't be too hard to connect them in the right way.
Is the second gyro broken as well? Could be possible of course but it's still very unlikely.
So I thought about the scanner but it's just copy&pasted from the link so it should work fine as well especially due to the fact that it worked for other people as well. The scanner is covering the addresses from 0 to 127 while my gyro should reply at address 104 so it should be convered.
So what is the problem here? I am really confused and a little desperated. Is there anything else I could try get at least a little closer to the problem? My problem there is that I dont have any other I²C sensors or Arduino devices or something I could try/replace my setup with.